Polygon ABCDE is reflected to produce polygon. A B C D E. what is the equation for the line of reflection

A balloon is blowing up at a constant rate of 9 cubic centimeters per second. When the volume of the balloon is 2048/3 pi cubic

jekas [21]

Answer:

$\displaystyle \frac{dr}{dt}\approx 0,0112\ cm/sec$

Step-by-step explanation:

<u>Rates of Change as Derivatives</u>

If some variable V is a function of another variable r, we can compute the rate of change of one with respect to the other as the first derivative of V, or

$\displaystyle V'=\frac{dV}{dr}$

The volume of a sphere of radius r is

$\displaystyle V=\frac{4}{3}\pi r^3$

The volume of the balloon is growing at a rate of $9\ cm^3/sec$ . This can be written as

$\displaystyle \frac{dV}{dt}=9$

We need to compute the rate of change of the radius. Note that both the volume and the radius are functions of time, so we need to use the chain rule. Differentiating the volume with respect to t, we get

$\displaystyle \frac{dV}{dt}=\displaystyle \frac{dV}{dr}\displaystyle \frac{dr}{dt}$

$\displaystyle \frac{dV}{dt}=4\pi r^2 \frac{dr}{dt}$

solving for $\displaystyle \frac{dr}{dt}$

$\displaystyle \frac{dr}{dt}=\frac{\frac{dV}{dt}}{4\pi r^2}$

We need to find the value of r, which can be obtained by using the condition that in that exact time

$\displaystyle V=\frac{2048}{3}\pi\ cm^3$

$\displaystyle \frac{2048}{3}\pi=\frac{4}{3}\pi r^3$

Simplifying and isolating r

$\displaystyle r^3=512$

$\displaystyle r=\sqrt[3]{512}=8\ cm$

Replacing in the rate of change

$\displaystyle \frac{dr}{dt}=\frac{9}{4\pi 8^2}$

$\displaystyle \frac{dr}{dt}=\frac{9}{256\pi }$

$\displaystyle \frac{dr}{dt}\approx 0,0112\ cm/sec$

8 0

2 years ago

Put into scientific notation 2910000

dolphi86 [110]

Answer:

The Answer is: 2.91 x 10^6

Step-by-step explanation:

Move the decimal from the right to left and count the number of moves, stopping at the next to last number.

Given:

2,910,000

In Scientific notation:

2.91 x 10^6

Hope this helps! Have an Awesome Day!! :-)

7 0

2 years ago

What is the average rate of change of the function f(x)=5(2)^x from x = 1 to x = 5?

Mila [183]

Average rate of change refers to the slope of a function/equation.
To solve this, plug in for both x values and calculate the average, or mean.

x = 1
f(1) = 5(2)^1
= 5(2)
= 10

x = 5
f(5) = 5(2)^5
= 5(32)
= 160

Now, you calculate the average:
10 + 160 = 170
Divide by 2 and you get 85.

5 0

2 years ago

What is the opposite of the opposite of -2

melisa1 [442]

Answer:

2 is the opposite of-2 and -2 is the opposite of 2

3 0

2 years ago

The point C(5, 4) is translated 9 units down.

Naily [24]

Answer:

The new point is at (5, -5)

Step-by-step explanation:

When a point is being translated down, they are being subtracted on the y-value. So all you have to do is subtract 9 from 4 and we end up with -5, our new y-value.

(5, -5)

3 0

2 years ago

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